X iv :m at h/ 04 09 13 9v 1 [ m at h. FA ] 8 S ep 2 00 4 A WEAK TYPE INEQUALITY FOR NON-COMMUTATIVE MARTINGALES AND APPLICATIONS NARCISSE RANDRIANANTOANINA Abstract. We prove a weak-type (1,1) inequality for square functions of noncommutative martingales that are simultaneously bounded in L and L. More precisely, the following non-commutative analogue of a classical result of Burkholder holds: ...

Let $R$ be a commutative ring with $1 \ne 0$ and let $m$ and
 $n$ integers $1\leq n < m$. A proper ideal $I$ of is
 called an $(m, n)$-closed if whenever $a^m \in I$ for
 some $a\in R$ implies $a^n I$. $ f:A\rightarrow B$ a
 homomorphism $J$ $B.$ This paper
 investigates the concept $(m,n)$-closed ideals in the
 amalgamation $A$ $B$ along respect $f$ denoted by&...

We introduce “embedding dimensions” of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II1 factor. These embedding dimensions are von Neumann algebra invariants, i.e., do not depend on the choices of the generators. We also find values of these invariants for some specific von Neumann algebras.

We prove that a finite von Neumann algebra A is semisimple if the algebra of affiliated operators U of A is semisimple. When A is not semisimple, we give the upper and lower bounds for the global dimensions of A and U . This last result requires the use of the Continuum Hypothesis.

An element in a ring is called clean if it may be written as a sum of a unit and idempotent. The ring itself is called clean if every element is clean. Recently, Anderson and Camillo (Anderson, D. D., Camillo, V. (2002). Commutative rings whose elements are a sum of a unit and an idempotent. Comm. Algebra 30(7):3327–3336) has shown that for commutative rings every von-Neumann regular ring as we...

Suppose F is a finite set of selfadjoint elements in a tracial von Neumann algebra M . For α > 0, F is α-bounded if Pα(F ) < ∞ where Pα is the α-packing entropy of F introduced in [7]. We say that M is strongly 1-bounded if M has a 1-bounded finite set of selfadjoint generators F such that there exists an x ∈ F with χ(x) > −∞. It is shown that if M is strongly 1-bounded, then any finite set of ...

in this paper we prove that each element of any regular baer ring is a sum of two units if no factor ring of r is isomorphic to z_2 and we characterize regular baer rings with unit sum numbers $omega$ and $infty$. then as an application, we discuss the unit sum number of some classes of group rings.

Suppose M is a tracial von Neumann algebra embeddable into R ω (the ultraproduct of the hyperfinite II 1-factor) and X is an n-tuple of selfadjoint generators for M. Denote by Γ(X; m, k, γ) the microstate space of X of order (m, k, γ). We say that X is tubular if for any ǫ > 0 there exist m ∈ N

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study in a broad sense: general critics on conventional logic by examining the essence of logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As...

We present a to following results in the constructive theory of operator algebras. A representation theorem for finite dimensional von Neumann-algebras. A representation theorem for normal functionals. The spectral measure is independent of the choice of the basis of the underlying Hilbert space. Finally, the double commutant theorem for finite von Neumann algebras and for Abelian von Neumann a...